Catherine Langevin Semel, Assistant District Attorney, for the Commonwealth.

BOTSFORD, J.

A jury convicted the defendant, Hector Guerrero Avila, of murder in the first degree on the theories of premeditation and extreme atrocity or cruelty and possession of a firearm without a license. On appeal, the defendant argues that the judge erred (1) in admitting testimonial and documentary evidence that had been introduced by the Commonwealth to rebut a defense based on the allegedly inadequate police investigation (Bowden defense1); (2) in admitting evidence used by the Commonwealth to prove deliberate premeditation and extreme atrocity or cruelty; (3) in admitting evidence about the contents of a telephone call allegedly made by the defendant the night before the murder; and (4) in declining to give an instruction to the jury based on Commonwealth v. Bowden,379 Mass. 472, 485-486 (1980) (Bowden). The defendant also raises certain claims under the standards set out in Commonwealth v. Moffett,383 Mass. 201, 216-217 (1981). We reject the defendant’s arguments and, after reviewing the entire case, decline to exercise our authority under G. L. c. 278, § 33E, to reduce the degree of guilt or order a new trial.

1. Background. The jury could have found the following. The defendant was close friends with Pedro Cruz, and in the fall of 2003, the two lived two blocks apart in Lawrence. The defendant and Cruz typically spoke to each other on the telephone several times a day and the defendant regularly spent time at Cruz’s apartment. Cruz drove a white Chevrolet Corsica automobile that the defendant had permitted Cruz to have registered in the defendant’s name in order for Cruz to obtain a lower insurance rate.

In October, 2003, Cruz was selling drugs in Lawrence with the assistance of the defendant. The defendant loaned Cruz money to be used for the purchase of cocaine, which Cruz stored in his home, repackaged into smaller quantities, and sold at a profit. At some point, the defendant introduced Cruz to Jose Crespo, the victim, whom Cruz knew only by the name of “Xavier.” The victim apparently stayed with Cruz in his apartment for some days, but also rented a room or apartment from Felipa Marquez. Marquez purchased drugs from Cruz, and the victim worked with Cruz in the sale of drugs. Cruz initially gave the victim drugs to sell, but after the victim failed to turn over to Cruz all the money from the sale of these drugs, Cruz arranged to have the victim telephone him when the victim had a buyer.

Some days after Cruz met the victim, Cruz traveled to New York. While Cruz was in New York, the defendant, who had access to Cruz’s apartment even when Cruz was not there, telephoned him to say that $1,000 of cocaine was missing from Cruz’s closet. According to Cruz, both he and the defendant suspected that the victim had taken the drugs. When Cruz returned from New York and mentioned the theft to the victim, he responded, “Oh well, you know, things happen.”

On November 5, 2003, the day before the murder, the defendant telephoned Cruz and told him that while he was at Cruz’s apartment that day, two men had broken in and attacked him with a knife. Cruz arrived home from his work to find that the defendant had cuts and bruises on his hands and back and that his apartment had been “torn apart”; there was “blood around all over.” The defendant told Cruz that he had chased the two men out of the apartment and had seen them get into a car driven by a third man. The defendant also told Cruz that the erratic way in which the driver had pulled out made the defendant think that the driver was the victim. As an apparent consequence of this supposition, the defendant and Cruz drove around in Cruz’s car, looking for the victim; the defendant had placed a baseball bat in Cruz’s car. When the defendant and Cruz were unsuccessful in finding the victim, the defendant told Cruz that he would like Cruz’s help looking for the victim the next day.

On November 6, the defendant telephoned Cruz and again asked him for help in looking for the victim; the defendant indicated that he wanted to determine if the victim was the person who had attacked him. Cruz telephoned his employer to say he would not be in for work. Cruz then received a telephone call from the victim, who asked whether Cruz could provide him with some cocaine to sell. Cruz told the victim that if the victim had the money, Cruz could supply the drugs, and the two agreed on a meeting place. When Cruz arrived at the meeting place, the victim left the car of his customer, entered Cruz’s car, gave Cruz some money, took the “stuff” back to his customer,2 returned to Cruz’s car, got in, and drove away with Cruz. Before meeting the victim, Cruz had telephoned the defendant to tell him that he would be seeing the victim.

As Cruz and the victim were driving, the defendant telephoned Cruz on Cruz’s cellular telephone, and Cruz described his location to the defendant. Soon afterward, the defendant telephoned Cruz again to tell him that he, the defendant, was directly behind Cruz and that Cruz should pull over. Cruz pulled over on Brook Street and told the victim that the defendant wanted to talk to him. The defendant parked his car, a brownish-grey Honda Civic automobile, a few feet behind Cruz’s white Corsica. The victim got out of Cruz’s car and walked toward the defendant’s car. Cruz got out of his car but remained near it; he was, however, near enough to the defendant and the victim to hear them talking.

The defendant asked the victim whether he had stolen money from the defendant and whether the victim had been part of the attack on him. The victim replied that he had not been involved. The defendant then pulled a gun out of a bag and shot the victim. At the time of this first shot, the defendant and the victim were approximately five to six feet apart, facing one another. The victim fell to the ground and then struggled to get up. The defendant extended his arm out toward the victim and shot him a second time. Cruz returned to his car and drove down Brook Street, passing a witness, Harry Milliken, who was standing in or near the street but past where the defendant’s and Cruz’s cars were parked, and who very soon thereafter reported the car’s registration plate number to the police.

At some point after Cruz left the scene, the defendant telephoned Cruz, told him that he, the defendant, was now in a different car, and arranged to meet him at a gasoline station in Methuen. When they met, the defendant told Cruz that the police had already been to the defendant’s home, having found his address through the registration plate number reported by Milliken to the police. The defendant encouraged Cruz to go to the police and tell them that the defendant had shot the victim because he was “scared for his life.” The defendant then drove Cruz to his sister’s house and left him there. Cruz stayed at his sister’s house for several hours and then drove with his brother to the Lawrence police station.

While at the police station that night, November 6, Cruz gave the first of three statements he would make to the lead police investigators on the case, Lawrence Detective Michael Laird and State Trooper Matthew Gravini. In this first statement, Cruz acknowledged that he had driven the victim to the scene of the shooting in the white Chevrolet Corsica, claimed that the shooter was an unknown black man who had driven there in a black Honda Prelude, and did not tell the police that the defendant was present at the scene or involved in the shooting.3 The police did not believe Cruz, or at least did not think Cruz was telling them all that he knew, and, with Cruz’s consent, they administered a lie detector test to Cruz the following day. He “failed” it.4

As a result of a lead developed from the subpoenaed telephone records, the police interviewed Marquez, the victim’s landlady, who described a telephone call she had received the night before the shooting from a Spanish-speaking male, warning her to not “let [the victim] in anymore” because “a very dangerous person is looking for [him] to kill him, because they gave him some material that he didn’t pay for.” Marquez used a feature on her telephone that allowed her to identify the number from which she had just been telephoned; the number was the same as the defendant’s cellular telephone number.

Approximately two weeks later, on November 20, 2003, the police went to Cruz’s workplace and interviewed him again, both at the workplace and at the police station. In this second interview, Cruz provided additional information but did not identify the defendant as the shooter. Later that night, Cruz telephoned Laird and told him that the defendant was the shooter. The next day, November 21, Cruz went to the police station, met with Laird and Gravini, and made a third statement. In it, he told the police about his close friendship with the defendant and connection to the victim, related to them details about the events that preceded the shooting, described the shooting itself, and reiterated his claim from the night before that the defendant was the shooter.5

Following Cruz’s third statement to the police, charges were brought against the defendant and, on December 18, 2003, he was arrested in New York City. Gravini traveled there with a Lawrence police officer to interview the defendant. After waiving his Miranda rights, the defendant made a statement denying that he had been on Brook Street on November 6, the day of the shooting, and also denying that he knew someone named Jose Crespo (the victim) or someone named “Xavier.”

At the scene of the shooting, the police recovered two spent shell casings, one spent projectile (bullet), and clothing that had been cut off the victim by emergency medical technicians. The bullet was found embedded in an article of that clothing, a leather jacket. A ballistician, Lieutenant Michael Coleman of the Massachusetts State police, took possession of the bullet and the two shell casings. After conducting tests on these three items and a second bullet recovered from the victim’s body during autopsy, Coleman concluded that both shell casings were discharged by the same weapon, and that both bullets also were fired from the same weapon. The bullet recovered from the leather jacket was severely damaged; it had a “flattened portion to it, consistent with striking a solid object.” The bullet recovered from the victim was in relatively good condition.

The victim’s clothing was examined by criminalist Paul J. Zambella of the Massachusetts State police crime laboratory. On the basis of his observations and testing of the clothing, Zambella concluded that at the time of the shooting, the victim was wearing a leather jacket over a sweater and a jersey. Zambella located two holes in the leather jacket, one in the back and one in the front and corresponding holes in the sweater and jersey as well. The bullet was embedded in the hole in the front of the jacket. Based on his examination of the hole in the back of the jacket, and of the melting and inward orientation of liner fibers near this hole, Zambella concluded that a weapon had been discharged while in contact with the back of the jacket.6

2. Discussion.

a. Rebuttal of defendant’s Bowden defense.

At trial, the defendant’s primary challenge to the Commonwealth’s case against him was built around a Bowden defense (see note 1, supra). See Bowden, 379 Mass. at 485-486.7 On appeal, the defendant claims that the judge committed errors in his handling of the Commonwealth’s rebuttal of his Bowden defense that require reversal of the defendant’s conviction.

(i) Background. The thrust of the defendant’s Bowden defense was that the police had obtained the defendant’s name (through the car registration plate number reported by Milliken) on the day of the murder, and had thereafter focused exclusively on the defendant in their investigation. As a result, the defense contended, the police failed to pursue strong leads pointing to other suspects and were too easily led astray by Cruz — an individual the defense characterized as far from truthful, probably involved in the murder himself, and therefore motivated to turn the investigative spotlight on the defendant. This was the theme of defense counsel’s opening statement, his closing argument, and substantial parts of his cross-examination of the two lead police investigators, Laird and Gravini.

When defense counsel questioned Laird on cross-examination about the failure of the police to investigate fully two other potential suspects, the judge permitted the questions, over the prosecutor’s hearsay objections, on the ground that they were relevant to the defendant’s Bowden defense. The judge twice gave limiting instructions to the jury, explaining that Laird’s testimony about what third parties had told him about these other suspects was not admitted for the truth of the matter, but for the sole purpose of allowing the jury to base their evaluation of the police investigation on an understanding of what the police knew.

On redirect examination, the prosecutor asked Laird when and why the police investigation began to focus on the defendant. Responding to the “when,” Laird testified that it was on November 21, 2003, because on that day, “we had [Cruz] putting the gun in [the defendant’s] hand and [Cruz] said that [the defendant] shot [the victim].” When the prosecutor then asked “what were the factors that drew you to focus your investigation on [the defendant],” the defendant objected. The judge ruled, however, that Laird could answer the question, concluding that in light of the defendant’s Bowden defense, the Commonwealth was permitted to elicit testimony about what led the police to conduct the investigation in a particular way.8 Laird then testified in substance that the police focused on the defendant on November 21, 2003, both because Cruz’s account of the shooting incident resonated with accounts of the incident given to police by other witnesses and because Cruz’s account of telephone calls between him and the defendant around the time of the shooting were consistent with the cellular telephone records obtained and examined by the police.

When Gravini testified, the prosecutor asked him a series of specific questions about what Cruz had said to the police investigators in his three statements, in response to which Gravini recounted much of each statement. The judge gave more than one limiting instruction, similar in content to those he gave during Laird’s testimony.

Gravini had taken notes of Cruz’s three statements to the investigators during the interrogations that took place on November 6, November 20, and November 21, respectively. He testified that his practice was to make written notes of everything a witness said verbatim, but not to make written notes of any of his own questions. Cruz had signed each of the three sets of notes taken by Gravini.9 Near the end of Gravini’s trial testimony, the prosecutor sought to introduce the written notes in evidence. Ultimately, the judge agreed that the notes could be admitted principally because they bore on the Bowden defense. The statements were then admitted as a trial exhibit, with redactions, over the objection of the defendant.

The judge instructed the jury at length that none of the evidence pertaining to Cruz’s statements to the police (i.e., the oral testimony of the investigators and Gravini’s notes) was being admitted substantively:

“Now in this case, you have a number of statements, both testified to orally by Mr. Cruz and that were apparently made in writing and signed by Mr. Cruz concerning the events of November sixth. Those were offered for a couple of purposes: one, to impeach the credibility of his in-court testimony to the extent that they may have been inconsistent with his in-court testimony and, two, so that you could see how his statement evolved over time, and use the information that the police had from those statements to assess the propriety of the actions which they took as they underwent their investigation. But the one thing you cannot use those statements for, you cannot use them as substantive evidence…. It is only Mr. Cruz’s in-court statements as to facts, which may be considered as substantive evidence of whether those facts occurred.”

(ii) Testimony concerning Cruz’s statements. “Defendants have the right to base their defense on the failure of police adequately to investigate a murder in order to raise the issue of reasonable doubt as to the defendant’s guilt in the minds of the jury.” Commonwealth v. Phinney,446 Mass. 155, 165-166 (2006), citing Bowden, 379 Mass. at 486. See Commonwealth v. Person,400 Mass. 136, 140 (1987) (“The defendant may expose any deficiencies in the police investigation. He may argue to the jury that, had the police done certain aspects of their investigation differently, it would have supported his defense”). See generally Commonwealth v. Silva-Santiago,453 Mass. 782, 801-802 (2009). Our cases make clear that if a defendant raises a Bowden defense, the Commonwealth has the right to rebut it. Commonwealth v. Lodge,431 Mass. 461, 467 (2000) (Lodge) (where “defendant has inserted into the case the relevance of the police judgment and decisions[,] the officer[s] must be allowed to defend that judgment”); Commonwealth v. Flanagan,20 Mass.App.Ct. 472, 476 n. 2 (1985) (Flanagan). See Commonwealth v. Silva-Santiago, supra at 803 n. 25. But determining precisely what evidence may be admitted to rebut a Bowden defense is a delicate and difficult task, given the fine line between permissibly allowing a police officer to explain investigative decisions (e.g., why certain leads were not followed, why certain tests were not conducted, why the police took their investigation in the direction that they did) and impermissibly allowing a police officer to offer an opinion about the guilt of the defendant, the credibility of a witness for the Commonwealth, or the strength of the Commonwealth’s case. See Lodge, supra at 467 (while Commonwealth may explain reasoning behind investigative decisions in response to Bowden defense, such testimony must be approached with caution and witness may not give opinion regarding culpability of defendant); Flanagan, 20 Mass. App. Ct. at 476 n. 2 (prosecutor’s questioning about reason for omission of test [or pursuit of investigative lead], “going to the subjective reasons for omission … should be approached with caution, lest it be made the vehicle for an improper expression of the officer’s opinion as to the need for such [test] in light of the strength of the case against the defendant”).

The defendant’s first argument is that under the guise of allowing the Commonwealth to respond to his Bowden defense, the judge erroneously allowed the prosecutor to elicit impermissible opinion testimony from both lead investigators about their views of the defendant’s guilt, as well as about the credibility of the Commonwealth’s primary witness, Pedro Cruz — with “overwhelming” prejudicial effect. See Lodge, supra at 467. We disagree.10

There is no question that the defendant forcefully and persistently raised his Bowden defense. Contrary to the defendant’s claim, however, the Commonwealth was not limited, in its rebuttal, to seeking explanations from the two police investigators about why they did not pursue the investigative leads that the defendant (through his counsel’s cross-examination) had put into play. As both the judge and this court have recognized,11 a Bowden defense is clearly a two-edged sword: the more wide-ranging the defendant’s attack on the police investigation, the broader the Commonwealth’s response may be. Here, the Bowden claim was an expansive one, calling into question police competence and judgment about both the leads that were not pursued and those that were. In response, the Commonwealth was entitled to elicit testimony about why the investigators chose the particular investigative path they did, including the reasons they ultimately accepted and acted on Cruz’s information that the defendant was the person who shot the victim.

The defendant focuses on Laird’s testimony that the police concentrated on the defendant after Cruz identified the defendant as the shooter in his third statement. By itself, this answer might perhaps be viewed as an implicit statement of opinion as to the defendant’s guilt or Cruz’s positive credibility, or both, but it was followed directly by questions and answers from Laird that explained more carefully the factors that led the police to focus on the defendant at that point: the information provided by Cruz in his third statement corresponded with the testimony of disinterested witnesses to the shooting and also with the cellular telephone records from that day. This is clearly different from the Lodge case, where the police detective responded to a general question with a comprehensive account of the evidence against the defendant. Lodge, 431 Mass. at 467 (detective’s answer provided impermissible “general expression of the officer’s opinion of guilt, followed by a recital of all the evidence against the defendant”). “[T]he prosecutor may proceed by inquiring of the officer the reason for each specific omission or decision.” Id. That is what happened here.

As for Gravini, as mentioned, the prosecutor elicited a great deal of testimony about the contents of Cruz’s three statements to the investigators. The defendant asserts that Gravini’s recitation of almost everything Cruz had told the police in his sequential statements was error because it served to express Gravini’s subjective opinion of (1) the defendant’s guilt and the catalog of reasons supporting that opinion, and (2) Cruz’s credibility. The argument fails to acknowledge the Commonwealth’s right, in the face of the defendant’s attack on the police decision to accept and act on Cruz’s ultimate statement, to trace and explain the investigators’ response to Cruz’s statements. The judge repeatedly instructed the jury that the investigators’ testimony about Cruz’s statements was presented to enable the jury to evaluate the police. We presume the jury abided by these instructions, see Commonwealth v. Jiles,428 Mass. 66, 74 (1998), and in the circumstances, we believe there is little risk that the jury took Gravini’s challenged testimony about Cruz’s statements as a confirmatory opinion of the defendant’s guilt.12

(iii) Written notes of Cruz’s statements. As previously indicated, near the end of the trial, after quite extensive discussion with counsel (out of the jury’s presence) and over the defendant’s objection, the judge admitted Gravini’s handwritten notes of Cruz’s three statements in evidence as an exhibit. At trial the defendant objected to the admission of the written statements on the grounds that they — and particularly the third — put in concrete form the version and chronology of events that were at the heart of the Commonwealth’s case, and would permit the jury to rely on the writings rather than their memory of Cruz’s testimony; he also argued that the statements were not everything Cruz said, but were instead a summary of Cruz’s statements, prepared by Gravini, the Commonwealth’s lead investigator. On appeal, the defendant raises these and additional arguments; in the latter category are his claims that in substance, the written version of the statements served as prior consistent statements that were inadmissible as such.13 He argues that the prejudice from the erroneous admission of the statements warrants reversal of his conviction.

The judge was correct that the presentation of a Bowden defense can expand the usual evidentiary boundaries quite significantly, permitting, as it does, the admission of evidence concerning information conveyed to the police by a wide variety of sources that would not or might not otherwise be admitted on hearsay or relevance grounds. See, e.g., Commonwealth v. Silva-Santiago, 453 Mass. at 803-804; Commonwealth v. Mathews,450 Mass. 858, 872 n. 15 (2008). Certainly a trial judge has broad discretion to admit or exclude evidence, including the discretion to exclude evidence on the ground that it is more prejudicial than probative. See Commonwealth v. Talbot,444 Mass. 586, 589 n. 2 (2005). While we recognize and respect that discretion, we conclude that the admission of the written statements in this case was error. The handwritten statement notes cover twenty pages. As defense counsel argued to the judge, there was a real risk that the jurors might substitute the written notes for their collective memory of Cruz’s testimony. Moreover, the notes represented the fourth presentation to the jury of Cruz’s version of events before, during, and after the shooting.14 The repetition increased the chance that the jury would inappropriately treat the oral and written evidence concerning Cruz’s statements as a form of credibility-enhancing prior consistent statement in relation to Cruz’s trial testimony. See Commonwealth v. Novo,449 Mass. 84, 93 (2007) (prior statement consistent with trial testimony usually inadmissible, because repetition of statement by witness ordinarily does not make it more trustworthy); Commonwealth v. Tennison,440 Mass. 553, 563 (2003) (same).

The Commonwealth contends that Cruz’s statements to the lead investigators, and the written notes of those statements, were admissible under the doctrine of verbal completeness; the claim is that the defense “opened the door” by cross-examining Cruz as well as the investigators about portions of Cruz’s statements, and therefore the Commonwealth was entitled to introduce the full statements to prevent misleading the jury by a fragmentary presentation. See Commonwealth v. Tennison, 440 Mass. at 563-564. The argument fails. The Commonwealth itself first introduced the topic of Cruz’s three statements to the police in the prosecutor’s direct examination of Cruz, Laird, and Gravini. That the defendant’s counsel followed up with questions about the statements in his cross-examination of each of these witnesses is hardly surprising, and in doing so, he did not open any door that had not already been opened. The doctrine of verbal completeness does not permit the Commonwealth, or any party, to ask a witness selective questions about a prior statement that itself would be inadmissible, and then secure the entire statement’s admission in evidence by claiming that the opposing party on cross-examination chose to ask other, equally selective questions about that same statement.

The defendant objected to the admission of the written notes at trial; the claim of error is therefore preserved. The resulting question is whether the error was prejudicial. See Commonwealth v. Flebotte,417 Mass. 348, 353 (1994). We are persuaded that it was not. While Cruz was a crucial witness for the Commonwealth — the only person who identified the defendant as the man who shot and killed the victim — Cruz himself was not a suspect for this role: the undisputed testimony of both disinterested eyewitnesses, Milliken and Ayala, was that the driver of the white Corsica, i.e., Cruz, was not the shooter. Moreover, Cruz’s three statements assisted the defense in one very significant way, because they necessarily reflected that Cruz had lied to the police repeatedly, as he was forced to acknowledge in his testimony. Further, while not dispositive, cf. Commonwealth v. Raymond,424 Mass. 382, 388 n. 6 (1997), relevant to this inquiry are the facts that (1) the jury had been introduced to virtually all the contents of Cruz’s statements through the testimony of Cruz, Laird, and Gravini — so that the notes were themselves cumulative of what had already been provided at trial in connection with the Bowden defense and its rebuttal; and (2) the judge repeatedly instructed the jury that, in accordance with the Bowden defense, they could not accept any of the evidence of Cruz’s statements as substantive proof of what Cruz stated, that is, for its truth. Finally, even though Cruz was a critical witness, the independently obtained evidence presented at trial — for example, the cellular telephone records of the defendant, Cruz, and certain others that the police had subpoenaed; the testimony of Pagan and Perez, who purchased cocaine from the victim shortly before he was killed; and the testimony of Milliken and Ayala, eyewitnesses at the scene of the shooting — offered repeated corroboration of the chronology of events that Cruz laid out and established a very strong case against the defendant. “We are confident that, if the error had not been made, the jury verdict would have been the same.” Lodge, 431 Mass. at 468. Cf. Commonwealth v. Raymond, supra at 388-389 (erroneous admission of prior consistent statement, not objected to at trial, did not create substantial likelihood of miscarriage of justice).

b. Expert testimony relating to victim’s manner of death.

The defendant argues that the prosecution proved its charge of murder in the first degree committed with deliberate premeditation and extreme atrocity or cruelty15 on the basis of inadmissible testimony offered by two expert witnesses: Dr. Mark Flomenbaum, then the chief medical examiner for the Commonwealth, but not the medical examiner who had conducted the victim’s autopsy; and Coleman, a ballistician for the State police. The defendant argues that “shorn of the challenged evidence, the government’s case for first degree murder would have collapsed” and asks this court to reduce the verdict from murder in the first degree to murder in the second degree.

(i) Medical examiner’s testimony concerning autopsy report. Dr. Abraham Philip, the medical examiner who conducted the victim’s autopsy in November, 2003, was no longer employed by the Commonwealth at the time of trial. Dr. Flomenbaum, then the chief medical examiner for the Commonwealth, testified at trial in Dr. Philip’s stead. Dr. Flomenbaum offered his opinions on direct examination that the “cause of death” was “the gunshot wounds through the aorta and kidney” and the “mechanism” of death was “hemorrhage” or “loss of blood.” He also offered an opinion on how long it might have taken the victim to die, and about whether the victim might have been conscious after each shot was fired. These opinions were based primarily on the autopsy report and an autopsy diagram prepared by Dr. Philip.16

Dr. Flomenbaum also testified on direct examination, based on the autopsy report and diagram, that one bullet entered on the left front side of the victim’s body, damaged the kidney, fractured a rib, and lodged on the right side of the body, just beneath the surface of the back; and that a second bullet entered the victim’s back on the right side, went through a spinal bone, injured the aorta, and exited the body on the right front side of his abdomen, leaving a “shored exit wound.” He explained that a shored exit wound is created when a bullet exits a body that is “shored up against” another surface and that such a wound has specific characteristics recognizable to an expert.

The defendant concedes that Dr. Flomenbaum’s opinions on the victim’s cause of death, the mechanism of death, and “how long it took [the victim] to die” were admissible. See Commonwealth v. Nardi,452 Mass. 379, 390-391 (2008) (Nardi). He argues, however, that Dr. Flomenbaum was not permitted to recite Dr. Philip’s findings and conclusions on direct examination, or to support or “buttress” his own opinions by setting out the facts and observations stated by Dr. Philip.17

In Nardi, we addressed the issue whether our rules of hearsay, as well as the confrontation clause of the Sixth Amendment to the United States Constitution, limit the types of testimony that may be offered by a medical examiner who did not perform the victim’s autopsy but who, in preparation for testifying, reviewed the autopsy report and related materials (substitute medical examiner). We held that the substitute medical examiner could offer an opinion as to the victim’s cause of death even though that opinion was based on the facts and findings in the autopsy report that was not itself admissible, Nardi, 452 Mass. at 390-391, but that the substitute medical examiner could not testify about these facts and findings themselves on direct examination. Id. at 392-393.

The victim’s cause of death in Nardi was hotly disputed, and our discussion in that case accordingly focused on whether the substitute medical examiner could permissibly offer opinion testimony on that one issue. However, as the defendant here concedes to some extent, a substitute medical examiner testifying as an expert is not limited to giving his or her own opinion as to cause of death only. Rather, substitute medical examiners may give their opinions on a wide range of subjects, based on their own review of autopsy reports, photographs, or other information gathered during an autopsy performed by another medical examiner. The substitute medical examiner’s opinions must be grounded in the evidence presented at trial, Commonwealth v. DelValle,443 Mass. 782, 791-792 (2005), but once that condition is met, he or she may offer opinions on such issues, among others, as whether a particular wound was an entry or exit wound, the amount of time that would have elapsed between injury and death, the amount of force required to inflict an injury, the characteristics of the object probably used to inflict the type of injury observed, and the effect that certain types of injuries would have had on the victim.

Expert opinion testimony of this nature is permissible as an evidentiary matter. “[Medical] examiners, as expert witnesses, may base their opinions on (1) facts personally observed; (2) evidence already in the record or which the parties represent will be admitted during the course of the proceedings, assumed to be true in questions put to the expert witnesses; and (3) `facts or data not in evidence if the facts or data are independently admissible and are a permissible basis for an expert to consider in formulating an opinion.'” Nardi, supra at 388, quoting Commonwealth v. Markvart,437 Mass. 331, 337 (2002). An expert with no firsthand knowledge of the facts at issue, such as a substitute medical examiner, “will not be able to testify factually, but will be asked to state an expert opinion based upon facts assumed in the questions put to [the expert] hypothetically, by sitting through the trial, or on the basis [of] certain qualifying data made available to the expert prior to the trial or hearing.” W.G. Young, J.R. Pollets & C. Poreda, Evidence § 703.1, at 503 (2d ed. 1998). An autopsy report is a “`permissible basis for an expert to consider in formulating an opinion’ … because `the underlying “facts or data” contained [therein] would potentially [be] admissible through appropriate witnesses.'” Nardi, supra at 389, quoting Commonwealth v. Markvart, supra. See United States v. De La Cruz,514 F.3d 121, 134 n. 5 (1st Cir. 2008), cert. denied, 129 S.Ct. 2858 (2009), quoting Crowe v. Marchand,506 F.3d 13, 17-18 (1st Cir. 2007) (“[A]s a matter of expert opinion testimony, a physician’s reliance on reports prepared by other medical professionals is `plainly justified in light of the custom and practice of the medical profession. Doctors routinely rely on observations reported by other doctors … and it is unrealistic to expect a physician, as a condition precedent to offering opinion testimony … to have performed every test, procedure, and examination himself'”). “The expert may, however, `be required to disclose the underlying facts or data on cross-examination,’ including that he did not personally conduct the relevant tests and examinations.” Nardi, supra at 390, quoting Commonwealth v. Daye,411 Mass. 719, 743 (1992).

Expert opinion testimony of this nature does not offend the confrontation clause as interpreted by the Supreme Court of the United States in Crawford v. Washington,541 U.S. 36 (2004) (Crawford) (confrontation clause prohibits admission of testimonial out-of-court statements unless declarant unavailable and defendant had prior opportunity to cross-examine declarant about statements), and most recently in Melendez-Diaz v. Massachusetts,129 S.Ct. 2527 (2009) (deeming certificates of forensic laboratory analysis offered in evidence in lieu of testimony as testimonial, and thus subject to Crawford, because certificates were affidavits prepared for sole purpose of serving as evidence at trial). To repeat, as we held in Nardi, the substitute medical examiner, as an expert witness, is not permitted on direct examination to recite or otherwise testify about the underlying factual findings of the unavailable medical examiner as contained in the autopsy report.18Nardi, supra at 394 (deeming statements in autopsy report testimonial hearsay barred by Crawford). The expert witness’s testimony must be confined to his or her own opinions and, as to these, the expert is available for cross-examination.

In the present case, and in accordance with Nardi, we conclude that the judge correctly permitted Dr. Flomenbaum to offer his opinions concerning issues related to the autopsy, but erred in allowing Dr. Flomenbaum to testify on direct examination about the findings in Dr. Philip’s autopsy report — both because these findings were inadmissible hearsay and because they violated the confrontation clause.19Id. at 391-396.20 We also conclude, however, that this unpreserved error21 did not result in a substantial likelihood of a miscarriage of justice. Commonwealth v. Wright,411 Mass. 678, 682 & n. 1 (1992). Contrary to the assertions of the defendant, the testimony admitted in error was distinctly cumulative. Other evidence independently supported the Commonwealth’s contention that the victim fell to the ground following the first shot; and that the defendant extended his arm toward the victim, now lying face down on the ground, and shot him in the back at close range.22

(ii) Medical examiner’s testimony about deformed bullet. At trial, the prosecutor asked Dr. Flomenbaum, “Based on your training and experience, to a reasonable degree of medical certainty, are you able to give the jurors an opinion as to whether [the deformed bullet] is consistent with having struck the pavement after leaving the body?” Defense counsel objected on the grounds that no foundation had been laid to establish that Dr. Flomenbaum was an expert in metallurgy and that his opinion exceeded the scope of his medical expertise. The judge overruled the objection and Dr. Flomenbaum replied, “I have an opinion that that bullet could have been deformed by hitting pavement or brick or some solid granular surface.” Defense counsel then moved to strike and the judge denied the motion.

There was no error. “A judge has wide discretion in qualifying a witness to offer an expert opinion on a particular question… and his determination will not be upset on appeal if any reasonable basis appears for it (citations omitted).” Commonwealth v. Rice,441 Mass. 291, 298 (2004), quoting Commonwealth v. Mahoney,406 Mass. 843, 852 (1990). See Commonwealth v. Devlin,365 Mass. 149, 152 (1974) (trial judge’s ruling on admission of expert testimony “will be reversed on appeal only if it constituted an abuse of discretion or was otherwise tainted with error of law”). Dr. Flomenbaum was board certified in both pathology and forensic pathology, had served as a medical examiner in New York, and had become the Commonwealth’s chief medical examiner in 2005. The defendant concedes that “[Dr.] Flomenbaum was arguably competent to testify that the bullet could not have been marred with fine pock marks by contact with any obstacle within the body.” Given the witness’s training and experience, the judge did not abuse his discretion in allowing Dr. Flomenbaum then to opine that these fine pockmarks could have been created outside the body by a granular surface such as pavement or brick. See Commonwealth v. Crouse,447 Mass. 558, 569-570 (2006). See also Commonwealth v. Sullivan, 17 Mass.App.Ct. 981, 982 (1984) (medical examiner, although not expert in ballistics, could permissibly offer opinion of distance from which fatal shot at been fired).

(iii) Ballistician’s testimony concerning deformed bullet. At trial, the prosecutor posed the following hypothetical to Coleman, the ballistician:

“Assume that an individual is shot, the bullet goes in through the back, it now progresses through the body, and now is coming out the front portion of the body. And you have this projectile that you recover, and you recover it from the jacket as you did, [and the jacket was worn by the person in a normal manner,23] are you able to form an opinion as to what, if any, surface that projectile hit, either within the body, or outside of the body based on your inspection of that projectile?”

Coleman replied, “For that projectile to stop at that point and sustain that type of damage, some solid contact such as pavement — the jacket would have to be in contact with something such as pavement to stop at that point and sustain that type of damage.”

The defendant objected at trial to the hypothetical. He argues here that the use of the hypothetical was error because it was based on facts that were not properly introduced into evidence. See Commonwealth v. Federico,425 Mass. 844, 850 & n. 11 (1997). In particular, he contends that there was no evidence that the victim was wearing the leather jacket, and that several of the facts assumed by the hypothetical were inadmissible hearsay inasmuch as their only source was the autopsy report of the original medical examiner, who did not testify.

It is true that a proper hypothetical question must be based on admissible evidence that has been or will be introduced. Commonwealth v. Rodriguez,437 Mass. 554, 564-566 (2002). We disagree, however, with the defendant’s claim that the hypothetical was based on facts not in evidence. First, there was evidence that the victim was wearing the jacket at the time of the shooting. Zambella testified without objection that he was told that all of the clothing he had collected, including the leather jacket, had been cut off the victim. Second, the record demonstrates that Dr. Philip was not the only source for some of the facts included in the hypothetical. Zambella’s opinion that a weapon was fired while in contact with the back of the jacket supplied evidence that, as the hypothetical posited, the bullets entered the victim’s body “through the back.” And Zambella’s opinion was based not on the autopsy report, but on his own examination of the hole in the back of the jacket and on the inward orientation of the liner fibers around this hole. Zambella also supplied evidence, independent of the autopsy; he observed the bullet protruding from the front of the jacket. It can reasonably be inferred from this evidence that the bullet entered the back of the jacket, traveled through the body, emerged from the front of the body, and became embedded in the front of the jacket.

The factual basis of the hypothetical was thus sufficient. Coleman’s response, that is, his opinion that the damage to the bullet could be explained only by positing that it had hit a hard surface such as pavement, fell within the scope of his training and experience (the defendant does not argue otherwise) and was therefore admissible.24

To conclude, our review of the various evidentiary errors that the defendant has raised in relation to evidence of the victim’s death persuades us that there is no basis for reducing the defendant’s verdict from murder in the first degree to murder in the second degree. See, e.g., Commonwealth v. DelValle, 443 Mass. at 797.

c. Evidence concerning telephone call purportedly made by defendant.

The defendant claims error in the admission of the testimony of Felipa Marquez concerning the contents of a telephone call that she received the night before the victim was killed.25 He argues that the statement, while proffered for a nonhearsay reason, namely, as evidence of the defendant’s state of mind, was too “ambiguous” to shed light on the caller’s state of mind; he posits that the telephone call could have been a warning to Marquez or a “tip-off” to the victim. The defendant claims further that the statement did not qualify as an admission because its “ambiguity eviscerated any probative value it might have offered regarding the defendant’s intent to kill [the victim],” and that it was unduly prejudicial.

There was no error. The evidence at trial would permit the jury reasonably to infer that the caller was the defendant,26 and the jury could also reasonably understand the statement as indicative of the defendant’s plan or intent to kill the victim. “Statements, not too remote in time, which indicate an intention to engage in particular conduct, are admissible to prove that the conduct was, in fact, put in effect.” Commonwealth v. Ferreira,381 Mass. 306, 310 (1980). See Mass. G. Evid. § 803(3)(B)(ii) (2008-2009). To the degree that the caller’s statement was ambiguous, the ambiguity went to the weight of the evidence, which is a matter reserved for the jury. See Commonwealth v. Cowels,425 Mass. 279, 285-286 (1997); Commonwealth v. Montecalvo,367 Mass. 46, 54 (1975), and cases cited.

d. Bowden instruction.

The defendant asserts that the judge, having told the jury members that they could consider various pieces of evidence to evaluate the quality of the police investigation and determine whether it was biased against the defendant, was duty bound to give the jury a Bowden instruction. See Bowden, 379 Mass. at 486. The defendant claims that the judge’s failure to give such an instruction impermissibly took the issue of a potentially faulty police investigation away from the jury. We disagree.

The Bowden case makes clear that a judge may not remove the issue of a biased or faulty police investigation from the jury, see id., but that is not what happened here. The judge carefully and repeatedly instructed the jury that certain pieces of evidence, including Cruz’s statements, were being admitted for the sole purpose of allowing the jury to evaluate whether the police investigation was biased or faulty. In Commonwealth v. Williams,439 Mass. 678, 687 (2003), we indicated that “Bowden’s only requirement” is that “the judge … not remove the inadequacy of the police investigation from consideration by the jury” and that “the giving of [a Bowden] instruction is never required” (emphasis added). The judge here acted within his discretion to decline a Bowden instruction.

(i) Jury instructions. The judge did not improperly omit the element of unlawful killing from his charge to the jury on murder in the first degree. The judge instructed the jury that the Commonwealth, in order to secure a conviction on either murder in the first or second degree, must show both that the defendant killed the victim and that the killing was unlawful, i.e., that the defendant did not act in self-defense.

The judge did not err in declining to instruct the jury on reasonable provocation manslaughter because the victim’s conduct toward the defendant did not rise to the level of provocation. For such an instruction to be appropriate, “[t]here must be evidence that would warrant a reasonable doubt that something happened which would have been likely to produce in an ordinary person such a state of passion, anger, fear, fright, or nervous excitement as would eclipse his capacity for reflection or restraint, and that what happened actually did produce such a state of mind in the defendant.” Commonwealth v. Walden,380 Mass. 724, 728 (1980). See Commonwealth v. Bertrand,385 Mass. 356, 363 (1982). There was no such evidence here.

The judge also did not err in failing to instruct on self-defense as a complete defense from criminal liability.27 The instruction was not requested, and the failure to give it did not result in a substantial likelihood of a miscarriage of justice. Further, no self-defense instruction was warranted because “[t]he right to self-defense does not arise unless,” inter alia, “the defendant took every opportunity to avoid combat.” Commonwealth v. Berry,431 Mass. 326, 335 (2000). In this case, the defendant arranged to meet the victim on a public street and arrived there in his own car. As the Commonwealth argues, quoting Commonwealth v. Pasteur,66 Mass.App.Ct. 812, 820 (2006), where “there is no evidence that the principal was not able to walk away, there is no basis for a claim of self-defense.”

Because the judge did not err with respect to these jury instructions on unlawful killing, provocation manslaughter, and self-defense, trial counsel was not ineffective for failing to challenge the jury instructions.

(ii) Daubert-Lanigan challenge to ballistics evidence. Trial counsel was not ineffective in failing to make a Daubert-Lanigan challenge to the ballistics testimony. Daubert v. Merrell Dow Pharms., Inc.,509 U.S. 579, 592-593 (1993); Commonwealth v. Lanigan,419 Mass. 15 (1994). At the time of the defendant’s trial and at present, there is a dearth of appellate or indeed any case law accepting a Daubert-Lanigan challenge to ballistics evidence. Moreover, while the defendant argues that there was a need for “photomicrographs” and additional documentation to support the ballistics testimony, he does not explain what this additional documentation would have shown or what it would have accomplished for his case. See Commonwealth v. Satterfield,373 Mass. 109, 115 (1977). There was no error.28

f. G. L. c. 278, § 33E.

We have reviewed the entire record and have found no grounds warranting relief under G. L. c. 278, § 33E.

Judgments affirmed.

Footnotes

1. A “Bowden defense” refers to a defense built around the proposition that an inadequate police investigation may raise serious questions about whether the police and the Commonwealth have charged and are prosecuting the proper perpetrator, and thus may give rise to reasonable doubt about the defendant’s guilt. See Commonwealth v. Bowden,379 Mass. 472, 485-486 (1980) (Bowden) (“The fact that certain tests were not conducted or certain police procedures not followed could raise a reasonable doubt as to the defendant’s guilt in the minds of the jurors”).

2. The two people in the car to which the victim brought the drugs were Miguel Perez and Ludim Pagan. Both testified at trial, and both testified consistently with Cruz in relation to the time and specifics of the drug sale and the victim’s role in it.

3. Cruz also provided the police with his and the defendant’s cellular telephone numbers, which they used to subpoena telephone records. See G. L. c. 271, § 17B.

4. A number of witnesses — two police officers and Cruz — testified about Cruz’s taking a lie detector test at the request of the police investigators and about some of the results of that test. This evidence was introduced and admitted without objection, presumably because the defense sought to use the fact that Cruz “failed” the test to the defendant’s advantage.

5. Cruz testified at trial to essentially the same facts as he stated to the police in his third statement. Cruz’s trial testimony is the evidentiary source of many of the facts summarized in the text, supra.

6. We set out additional facts hereafter in connection with our discussion of the issues raised.

7. Although the defense in Bowden itself focused on the alleged failure of the police to conduct tests or follow regular investigatory procedures, see Bowden, 379 Mass. at 485-486, a Bowden defense is not limited to these issues. “We have recognized that the failure of the police to investigate leads concerning another suspect is sufficient grounds for a Bowden defense.” Commonwealth v. Silva-Santiago,453 Mass. 782, 802 (2009), citing Commonwealth v. Phinney,446 Mass. 155, 166 (2006), and Commonwealth v. Reynolds,429 Mass. 388, 391-392 (1999).

8. In a sidebar conference on the issue, the judge stated: “Of course in a normal case a police officer would never be able to summarize the factors that in his mind pointed to the guilt of the defendant but here there is a direct challenge to the motives of the police and I do think that the Commonwealth has the right to have them then elicit what motives other than bias, what factors other than bias led them to head in a certain direction. So I think it is permissible. I mean that is — the upside of a Bowden Defense is it’s very powerful and juries are very accepting of it but the downside is I think it does open up the right of the Commonwealth to go into police officers’ thoughts and so forth.”

9. None of the interviews with Cruz was recorded on audiotape or videotape.

10. The defendant objected to certain portions of Detective Laird’s and Trooper Gravini’s testimony, but not to all of the testimony that he challenges on appeal. Because we conclude there was no error, we do not need to decide whether the standard of review is prejudicial error, see, e.g., Commonwealth v. Flebotte,417 Mass. 348, 353 (1994), or a substantial likelihood of a miscarriage of justice, see, e.g., Commonwealth v. Raymond,424 Mass. 382, 388-389 (1997).

11. See Commonwealth v. Silva-Santiago, 453 Mass. at 803 n. 25.

12. We reiterate, however, the need to use caution in assessing the scope of a rebuttal to a Bowden defense. Even where a Bowden defense is broad, it does not mean that the case becomes devoid of evidentiary constraint. As appellate decisions have noted, the prospect of rebuttal to a Bowden defense should raise cautionary flags, because there is always the potential that the rebuttal evidence may come close to or cross the line between a permissible account of the police investigators’ rationale for pursuing a certain suspect or investigatory direction, and an impermissible expression of opinion of the defendant’s guilt or implicit comment on a witness’s credibility. See Commonwealth v. Lodge,431 Mass. 461, 467 (2000); Commonwealth v. Flanagan,20 Mass.App.Ct. 472, 476 n. 2 (1985). Cf. Commonwealth v. Ianello,401 Mass. 197, 202 (1987) (expert witness may not offer opinion as to witness’s credibility; witness credibility evaluations are for jury).

13. The defendant also argues that the written statements included some portions that were highly prejudicial to the defendant, and that the jury were able to consider these portions for the truth of their contents because the judge gave no limiting instruction. However, as indicated in the text, supra, the record is clear that the judge did in fact give a very specific limiting instruction on this precise subject.

14. The jury first heard the version from Cruz directly; the second time was through the testimony of Laird; the third time was through Gravini’s testimony; and the written notes were the fourth.

15. The Commonwealth, in its closing statement, suggested that the victim had been “executed.”

16. The autopsy diagram, but not the autopsy report, was admitted in evidence at trial.

17. For example, Dr. Mark Flomenbaum explained his opinion that the victim was alive at the time of the gunshot from the rear by pointing to “the quantity of blood that bled out when his heart was beating.” The defendant asserts that it was error to permit this testimony.

18. “If the defendant chooses to inquire about the basis for the testimony upon cross-examination, then the basis comes in; otherwise, the expert may give a conclusion but cannot describe the inadmissible basis for the opinion. In many circumstances, this may be as sensible an approach to balancing the competing concerns as any.” D.H. Kaye, D.E. Bernstein, J.L. Mnookin, The New Wigmore: A Treatise on Evidence — Expert Evidence § 3.10.8, at 64 (Supp. 2009).

19. The Commonwealth concedes that under Commonwealth v. Nardi,452 Mass. 379, 391 (2008) (Nardi), some of Dr. Flomenbaum’s direct testimony is inadmissible because it recites the facts and findings of Dr. Abraham Philip’s autopsy report. The Commonwealth acknowledges, in particular, that Dr. Flomenbaum’s testimony about the “shored exit wound” may have been inadmissible. We note that Dr. Flomenbaum testified twice on direct examination about the shored exit wound on the victim’s torso. On the first occasion, his testimony was based on the autopsy report and therefore was inadmissible. On the second occasion, however, Dr. Flomenbaum opined that the wound depicted in a photograph taken during the autopsy and admitted into evidence as an exhibit was a shored exit wound. It is not clear whether Dr. Flomenbaum would have been able to offer his opinion that the wound was a shored exit wound based on the photograph alone; if he could have, that opinion clearly would be admissible. Moreover, it was entirely permissible for Dr. Flomenbaum to explain in general what a “shored exit wound” is.

20. It is uncontested that the findings in the autopsy report were hearsay. See Nardi, 452 Mass. at 393-394. The statements made by Dr. Philip in the autopsy report were testimonial because “a reasonable person in [Dr. Philip’s] position would anticipate his [findings and conclusions] being used against the accused in investigating and prosecuting a crime.” Id. at 394, quoting Commonwealth v. Gonsalves,445 Mass. 1, 3 (2005), cert. denied, 548 U.S. 926 (2006).

21. The only time the defendant objected to the prosecutor’s questioning of Dr. Flomenbaum was when Dr. Flomenbaum was asked for his opinion whether the deformation of the bullet retrieved from the victim’s jacket was consistent with the bullet having struck pavement. See discussion of that point, infra.

22. Harry Milliken, one of the eyewitnesses, testified that he heard a “crack,” saw a man fall to the ground, saw an individual extend his arm toward the fallen man, and then heard a second crack. Zambella, the criminalist, testified that a weapon was fired while in contact with the back of the jacket.

23. This assumed fact was interposed by the judge.

24. As stated at the outset of Part 2 (b), the defendant asserts that the evidentiary errors he raises in connection with Dr. Flomenbaum’s and Coleman’s testimony affect the Commonwealth’s proof of murder in the first degree on the theory of deliberate premeditation as well as extreme atrocity or cruelty. It appears, however, that the thrust of his argument focuses almost exclusively on the Commonwealth’s proof of extreme atrocity or cruelty. In any event, quite apart from the testimony of Dr. Flomenbaum and Coleman, there clearly was ample evidence to support a theory of deliberately premeditated murder.

25. Felipa Marquez testified that the caller was a Spanish-speaking male who told her not to let the victim into her house any more because “a very dangerous person is looking for [him] to kill him, because they gave him some material that he didn’t pay for.”

26. There was abundant evidence that the telephone number that appeared on Marquez’s telephone as the caller’s was the same as the defendant’s cellular telephone number.

27. The judge did instruct on excessive use of force in self-defense, one theory of voluntary manslaughter. In particular, he told the jury that evidence that the defendant shot the victim in self-defense would render the defendant liable for manslaughter, as opposed to murder, but would not “excuse the defendant outright from criminal liability.”

28. The defendant argues, citing United States v. Sepulveda,15 F.3d 1161, 1195-1196 (1st Cir. 1993), and United States v. Fernandez,145 F.3d 59, 66 (1st Cir. 1998), that even if none of the issues raised in his Moffett brief is sufficient in isolation to warrant a new trial, these same issues might warrant a new trial when viewed cumulatively. Because we find that the judge did not commit the errors claimed, we have no reason to consider cumulative effect.